Advances in Sensitivity Analysis and Parametric Programming / Edition 1

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The numerous advances in mathematical programming have opened up new insights about sensitivity analysis. The paradigm 'What if...?' question is no longer the only question of interest. Often, we want to know 'Why...?' and 'Why not...?' Such questions were not analyzed in the early years of mathematical programming to the same extent that they are now, and we have not only expanded our thinking about 'post-optimal analysis', but also about 'solution analysis', even if the solution obtained is not optimal.
Therefore, it is now time to examine all the recent advances on sensitivity analysis and parametric programming. This book combines the origins of sensitivity analysis with the state of the art. It covers much of the traditional approaches with a modern perspective, and shows recent results using the optimal partition approach, stemming from interior methods, for both linear and quadratic programming. It examines the special case of network models. It presents a neglected topic, qualitative sensitivity analysis, as well as elements of mixed integer programming and gives a modern perspective of nonlinear programming. It provides recent advances in multi-criteria mathematical programming and also describes the state-of-the-art in shastic programming. It covers recent advances in understanding redundancy in quadratic programs, considers an approach to diagnosing infeasibility in linear and nonlinear programs, and gives an overview of sensitivity analysis for fuzzy mathematical programming.

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Editorial Reviews

Reports recent developments in the field made possible by interior point methods for linear programming. Includes a concise history, a general systems view, modern perspectives on traditional approaches in linear programming, recent results using the optimal partition approaches stemming from interior methods for both linear and quadratic programming, the special case of network models and how they lend themselves to special solution analysis, and qualitative sensitivity analysis. Also describes developments in related fields, such as mixed integer programming, non-linear programming using modeling languages, multi-criteria mathematical programming, stochastic programming and its application to financial models, redundancy in quadratic programs, diagnosing infeasibility in linear and nonlinear programs, and sensitivity analysis for fuzzy mathematical programming. Annotation c. by Book News, Inc., Portland, Or.
From the Publisher
'... well-organized book can be highly recommended to all who are engaged in operations research and decision making with incomplete information and/or multiple criteria. I do not hesitate to congratulate the two editors on their excellent work.'
OR Spektrum, 22 (2000)
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Product Details

Table of Contents

About the Authors
1 A Historical Sketch on Sensitivity Analysis and Parametric Programming
2 A Systems Perspective: Entity Set Graphs
3 Linear Programming 1: Basic Principles
4 Linear Programming 2: Degeneracy Graphs
5 Linear Programming 3: The Tolerance Approach
6 The Optimal Set and Optimal Partition Approach
7 Network Models
8 Qualitative Sensitivity Analysis
9 Integer and Mixed-Integer Programming
10 Nonlinear Programming
11 Multi-Criteria and Goal Programming
12 Stochastic Programming and Robust Optimization
13 Redundancy
14 Feasibility and Viability
15 Fuzzy Mathematical Programming
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